Poisson Distribution

In probability theory and statistics, the Poisson distribution (pronounced ) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event. (The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.)

For instance, suppose someone typically gets on the average 4 pieces of mail per day. There will be, however, a certain spread: sometimes a little more, sometimes a little less, once in a while nothing at all. Given only the average rate, for a certain period of observation (pieces of mail per day, phonecalls per hour, etc.), and assuming that the process, or mix of processes, that produce the event flow are essentially random, the Poisson distribution specifies how likely it is that the count will be 3, or 5, or 11, or any other number, during one period of observation. That is, it predicts the degree of spread around a known average rate of occurrence.

The distribution's practical usefulness has been described by the Poisson law of large numbers.

Read more about Poisson DistributionHistory, Definition, Related Distributions, Occurrence, Generating Poisson-distributed Random Variables, Bivariate Poisson Distribution

Other articles related to "poisson distribution, distribution, distributions, poisson":

Conway–Maxwell–Poisson Distribution - Generalized Linear Model
... The basic COM-Poisson distribution discussed above has also been used as the basis for a generalized linear model (GLM) using a Bayesian formulation ... A dual-link GLM based on the CMP distribution has been developed, and this model has been used to evaluate traffic accident data ... (2008) is based on a reformulation of the CMP distribution above, replacing with ...
Bivariate Poisson Distribution
... This distribution has been extended to the bivariate case ... The generating function for this distribution is with The marginal distributions are Poisson( θ1 ) and Poisson( θ2 ) and the correlation coefficient is limited to the range ...
Self-similar Process - The Poisson Distribution
... Before the heavy-tailed distribution is introduced mathematically, the Poisson process with a memoryless waiting-time distribution, used to model (amo ... terminations leads to the following The number of call arrivals in a given time has a Poisson distribution, i.e ... For this reason, pure-chance traffic is also known as Poisson traffic ...
Stirling Numbers Of The Second Kind - Applications - Moments of The Poisson Distribution
... If X is a random variable with a Poisson distribution with expected value λ, then its nth moment is In particular, the nth moment of the Poisson distribution with expected value 1 is ...
Conway–Maxwell–Poisson Distribution
... The COM-Poisson distribution was originally proposed by Conway and Maxwell in 1962 as a solution to handling queueing systems with state-dependent service rates ... The probabilistic and statistical properties of the distribution were published by Shmueli et al ... The COM-Poisson is defined to be the distribution with probability mass function for x = 0,1,2.. ...

Famous quotes containing the word distribution:

    There is the illusion of time, which is very deep; who has disposed of it? Mor come to the conviction that what seems the succession of thought is only the distribution of wholes into causal series.
    Ralph Waldo Emerson (1803–1882)